This paper discusses results from the second phase of the European Ice Sheet Modelling Initiative (EISMINT). It reports the intercomparison of ten operational ice-sheet models and uses a series of experiments to examine the implications of thermomechanical coupling for model behaviour. A schematic, circular ice sheet is used in the work which investigates both steady states and the response to stepped changes in climate. The major finding is that the radial symmetry implied in the experimental design can, under certain circumstances, break down with the formation of distinct, regularly spaced spokes of cold ice which extended from the interior of the ice sheet outward to the surrounding zone of basal melt. These features also manifest themselves in the thickness and velocity distributions predicted by the models. They appear to be a common feature to all of the models which took part in the intercomparison, and may stem from interactions between ice temperature, flow and surface form. The exact nature of these features varies between models, and their existence appears to be controlled by the overall thermal regime of the ice sheet. A second result is that there is considerable agreement between the models in their predictions of global-scale response to imposed climate change.

An indirect methodology for determining the distribution of mass balance at high spatial resolution using remote sensing and ice-flow modelling is presented. The method, based on the mass-continuity equation, requires two datasets collected over the desired monitoring interval: (i) the spatial pattern of glacier surface-elevation change, and (ii) the mass-flux divergence field. At Haut Glacier d’Arolla, Valais, Switzerland, the mass-balance distribution between September 1992 and September 1993 is calculated at 20 m resolution from the difference between the pattern of surface-elevation change derived from analytical photogrammetry and the mass-flux divergence field determined from three-dimensional, numerical flow modelling constrained by surface-velocity measurements. The resultant pattern of mass balance is almost totally negative, showing a strong dependence on elevation, but with large localized departures. The computed distribution of mass balance compares well (R2 = 0.91) with mass-balance measurements made at stakes installed along the glacier centre line over the same period. Despite the highly optimized nature of the flow-modelling effort employed in this study, the good agreement indicates the potential this method has as a strategy for deriving high spatial and temporal-resolution estimates of mass balance.

Modeling the reflectance and transmittance of strong volume scatterers is a delicate task. Slightly different approaches can lead to different results, making comparisons difficult. Here a simple, analytic multiple-scattering model is presented as a possible reference for comparisons and also for better understanding of the physics involved. The model quantifies the transmittance and reflectance of homogeneously distributed scatterers within slabs of any thickness. The simplicity of the model is given by the one-dimensional geometry, a system consisting of freely arranged ice lamellae in air. Although direct application of the model will be limited, it gives a spectral description of ice clouds and snowpacks over a very broad spectral range from microwave to ultraviolet. As well as the transmittance and reflectance, the model gives the emittance through Kirchhoff’s law. Comparison with other models shows, on the one hand, agreement with current snow models in the spectral description, and on the other, some quantitative inconsistencies between all of them. It appears that the lamella pack produces the same optical spectra as an average snow model, with spherical ice grains whose radius corresponds to about the lamella thickness, whereas microwave spectra appear to be slightly different.

Medial moraines form striking dark stripes that widen non-linearly, steepen laterally and increase in relief down-glacier from the equilibrium line. Coalescence of these low-ablation-rate features can feed back strongly on the mass balance of a glacier snout. Ablation-dominated medial moraines originate from debris delivered to glacier margins, producing a debris-rich septum between tributary streams of ice below their confluence. Emergence of this ice below the equilibrium line delivers debris to the glacier surface, which then moves down local slopes of evolving morainal topography. A quantitative description of moraine evolution requires specification of the debris concentration field within the glacier, treatment of the melt-rate dependence on debris thickness, and characterization of processes that transport debris once it emerges onto the ice surface. Debris concentration at glacier tributary junctions scales with the erosion rates and the lengths of the tributary-valley walls, and inversely with the tributary ice speeds. Melt rate is damped exponentially by debris, with a ∼10 cm decay scale. Debris flux across the glacier surface scales with the product of debris thickness and local slope. Analytical and numerical results show that medial moraines should develop cross-glacier profiles with parabolic crests and linear slopes, and should widen with age and hence distance down-glacier. Debris should be both thin and uniform over the moraine. Observed faster-than-linear growth of moraine widths with distance reflects the increasing ablation rate down-glacier. Increase in medial moraine cover reduces the local average ablation rate, allowing the glacier to extend further down-valley than meteorology alone would suggest. This feedback is especially effective when moraines merge.

The evolution of an inter-ice-stream ridge flanked by stagnated ice streams is simulated using a finite-difference, continuity ice-flow model. The model tracks the elevation of small-scale topographic undulations on the ice surface (“scars”) which form at ice-stream margins, and shows that after ice-stream stagnation these surface features are lifted onto the flanks of the evolving ridge before they are carried downslope by ice flow. The model is applied to the stagnant ice streams bounding Siple Dome, West Antarctica: “Siple Ice Stream” (SIS) on the northeast flank near Ice Stream D, and the “Duckfoot” area (DF) on the south flank near Ice Stream C. The volume-adjustment time-scale corresponding to the evolution of Siple Dome and these stagnant ice-stream areas is 1500–2000 years. The present geometry and elevation of the scar features, in addition to measurements of the present mass flux across the ridge, are used to estimate stagnation ages for SIS and DF. These measurements suggest that both SIS and DF stagnated 200–500 years ago.

Black Rapids Glacier is a 40 km long surge-type glacier in the central Alaska Range. In spring 1997 a wireline drill rig was set up at a location where the measured surface velocities are high and seasonal and annual velocity variations are large. The drilling revealed a layer of subglacial “till”, up to 7 m thick, that is believed to be water-saturated. At one location a string of instruments, containing three dual-axis tiltmeters and one piezometer, was successfully introduced into the till. The tiltmeters monitored the inclination of the borehole at the ice–till interface and at 1 and 2 m into the till, for 410 days. They showed that no significant deformation occurred in the upper 2 m of the till layer, and no significant amount of the basal motion was due to sliding of the ice over the till. The measured surface velocity at the drill site is about 60 m a−1, of which 20–30 m a can be accounted for by ice deformation. Almost the entire amount of basal motion, 30–40 m a−1, was taken up at a depth of > 2 m in the till, possibly in discrete shear layers, or as sliding of till over the underlying bedrock. We propose that the large-scale mobilization of such till layers is a key factor in initiating glacier surges.

Spatial and temporal variations of surface albedo on Haut Glacier d’Arolla, Switzerland, during the 1993 and 1994 ablation seasons are described. Correlation and regression analyses are used to explain the albedo variations in terms of independent meteorological and surface property variables. Parameterizations are developed which allow estimation of albedo variation in surface energy-balance models. Snow albedo is best estimated from accumulated daily maximum temperatures since snowfall. On “deep” snow (≥0.5 cm w.e. depth) a logarithmic function is used, while on “shallow” snow (<0.5 cm w.e. depth) an exponential function is used to enable the albedo to decay to the underlying ice or debris albedo. The transition from “deep” to “shallow” snow is calculated as a function of decreasing snow depth (combined r2 = 0.65). This new parameterization performs better than earlier schemes because accumulated daily maximum temperatures since snowfall correlate strongly with snow grain-size and impurity concentration, the main physical controls on snow albedo. Ice albedo may be parameterized by its relationship to elevation (r2 = 0.28), but this approach results in only a small improvement over the assumption of a constant mean ice albedo.

The acoustic televiewer is a geophysical logging instrument that is deployed in a water-filled borehole and operated while trolling. It generates a digital, magnetically oriented image of the borehole wall that is developed from the amplitudes and transit times of acoustic waves emitted from the tool and reflected at the water–wall interface. The transit-time data are also converted to radial distances, from which cross-sectional views of the borehole shape can be constructed. Because the televiewer is equipped with both a three-component magnetometer and a two-component inclinometer, the borehole’s trajectory in space is continuously recorded as well. This instrument is routinely used in mining and hydrogeologic applications, but in this investigation it was deployed in two boreholes drilled into Upper Fremont Glacier, Wyoming, U.S.A. The acoustic images recorded in this glacial setting are not as clear as those typically obtained in rocks, due to a lower reflection coefficient for water and ice than for water and rock. Results indicate that the depth and orientation of features intersecting the boreholes can be determined, but that interpreting their physical nature is problematic and requires corroborating information from inspection of cores. Nevertheless, these data can provide some insight into englacial structural characteristics. Additional information derived from the cross-sectional geometry of the borehole, as well as from its trajectory, may also be useful in studies concerned with stress patterns and deformation processes.

Ice single crystals of various orientations containing various concentrations of H2SO4 up to 11.5 ppm were cut from large pucks of laboratory-grown ice. Constant-strain-rate compression tests were performed on the doped ice crystals both at −20°C at an axial strain rate of 1 × 10−5 s−1 and at −10°C at 1 × 106 s−1. The stress–strain curves showed a linearly rising stress with increasing strain, followed by a sharply declining stress after reaching a peak. With further strain, the sharp decline in stress slowed. The tests clearly showed, for the first time, that this naturally occurring impurity dramatically decreases both the peak stress and the subsequent flow stress of ice single crystals. The decrease in the peak strength was related to the square root of the concentration of H2SO4 up to 11.5 ppm, suggesting that the solubility limit of H2SO4 in ice is at least 11.5 ppm. The sulfuric acid also appeared to increase the ductility of the ice. Preliminary examination of a doped ice single crystal by synchrotron X-ray topography suggested that sulfuric acid dramatically increases the grown-in dislocation density.

Numerous studies of the ice caps in Greenland and Antarctica have observed accumulations of transuranic radionuclides and fission products from nuclear weapons testing, particularly during the period 1945–75. Recently, the concentrations of radionuclides in the annually deposited surface layers of Agassiz Ice Cap, Ellesmere Island, Canadian Arctic, from 1945 to the present have been measured and have demonstrated a continuous record of deposition of 137Cs and 239,240Pu in ice and snow. In this study, 3He-ingrowth mass spectrometry has been used to measure the low levels of tritium (3H) in some of these samples. Pre-nuclear-bomb tritium levels in ice-core samples were approximately 12 TU in high-latitude meteoric waters and 3–9 TU in mid-latitude meteoric waters. Comparisons of 3H levels and 3H/137Cs + 239,240Pu ratios, which were quite low during the earliest fission-bomb detonations (1946–51) and substantially higher during thermonuclear hydrogen-fusion bomb testing (1952–64), provide a clear indication of the type of nuclear device detonated. This finding accords with the results from other ice-core studies of the distribution of anthropogenic radionuclides from bomb fallout.

One crucial condition for the interpretation of ice-core records is the establishment of an accurate time-scale. This task is especially difficult for glacier sites in a complex topography such as the Alps, due to the often irregular deposition of fresh precipitation. In this work, dating techniques were applied to an Alpine ice core from upper Grenzgletscher, Monte Rosa massif (4200 m a.s.l.), representing about two-thirds of the total glacier thickness. They are based on (i) the radioactive decay of the isotope 210Pb, (ii) seasonally varying signals such as the concentrations of NH4+ and the isotopic ratio δ18O, and (iii) stratigraphic markers from Saharan dust falls, atmospheric nuclear weapon tests and the reactor accident in Chernobyl. From the combined application of these dating methods, a time period of 1937–94 covered by the ice core was derived. Dating uncertainty is <1 year for the period 1970–94 and ± 2 years for the period 1937–69. The observed thinning of the annual layers as a function of depth could be well described by a simple kinematic glacier flow model.

The mean, steady-state particle velocity in gravity-driven glacial flow over sinusoidal, sloping ground is computed using a Lagrangian description of motion. A Newtonian viscous fluid approximation is used for the ice. The glacier surface is free to move and is not subject to any stresses. At the bottom, the ice is frozen to the ground. The non-linear interaction between the basic downslope Poiseuille flow and the bottom corrugations yields a mean Lagrangian perturbation velocity that is always directed in the upslope direction near the ground. The requirement of mass balance imposes a mean negative surface slope in the corrugated region and an associated downslope perturbation flow in the upper part of the glacier. The no-slip condition at the wavy bottom induces a strong velocity shear in the ice, and particularly at the base. Analysis shows that the shear heating associated with shortwave perturbations could, in the case of a marginally frozen ground, lead to melting and subsequent sliding at wave crests along the bottom, while the ice stays frozen at the troughs. It is suggested that for glaciers the resulting high strain rates could lead to crevassing.

A numerical model of the ice-sheet/ice-shelf transition was used to investigate ice-sheet dynamics across the large subglacial lake beneath Vostok station, central East Antarctica. European Remote-sensing Satellite (ERS-1) altimetry of the ice surface and 60 MHz radio-echo sounding (RES) of the ice-sheet base and internal ice-sheet layering were used to develop a conceptual flowline across the ice sheet, which the model used as input. The model calculates horizontal and vertical velocities and stresses, from which particle flow paths can be obtained, and the ice-sheet temperature distribution. An inverse approach to modelling was adopted, where particle flow paths were forced to match those identified from internal RES layering. Results show that ice dynamics across the inflow grounding line are similar to an ice-sheet/ice-shelf transition. Model particle flow paths match internal RES layering when ice is (a) taken away from the ice base across the first 2 km of the flowline over the lake and (b) added to the base across the remainder of the lake. We contend that the process causing this transfer of ice is likely to be melting of ice and freezing of water at the ice–water interface. Other explanations, such as enhanced rates of accumulation over the grounding line, or three-dimensional convergent/divergent flow of ice are inconsistent with available measurements. Such melting and refreezing would be responsible for circulation and mixing of at least the surface layers of the lake water. Our model suggests that several tens of metres of refrozen “basal ice” would accrete from lake water to the ice sheet before the ice regrounds.

We propose to quantify the climate sensitivity of the mean specific balance B of a glacier by a seasonal sensitivity characteristic (SSC). The SSC gives the dependence of B on monthly anomalies in temperature and precipitation. It is calculated from a mass-balance model. We show and discuss examples for Franz-Josef Glacier (New Zealand), Nigardsbreen (Norway), Hintereisferner (Austria), Peyto Glacier (Canadian Rockies), Abramov Glacier (Kirghizstan) and White Glacier (Canadian Arctic). With regard to the climate sensitivity of B, the SSCs clearly show that summer temperature is the most important factor for glaciers in a dry climate. For glaciers in a wetter climate, spring and fall temperatures also make a significant contribution to the overall sensitivity. The SSC is a 2 × 12 matrix. Multiplying it with monthly perturbations of temperature and precipitation for a particular year yields an estimate of the balance for that year. We show that, with this technique, mass-balance series can be (re)constructed from long meteorological records or from output of atmospheric models.

Since 1 October 1995, an automatic weather station has been operated on the tongue of Morteratschgletscher, Switzerland. The station stands freely on the ice, and sinks with the melting glacier surface. It is located at 2100 m a.s.l., and measures air temperature, wind speed and direction, incoming and reflected solar radiation, pressure and snow temperature. A sonic ranger, mounted to stakes drilled into the ice, measures surface height from which melt rates and snow accumulation can be derived. In this paper the data for the period 1 October 1995 to 30 September 1998 are used to evaluate the surface energy balance. The turbulent energy fluxes are calculated with the bulk method. The turbulent exchange coefficient Ch is used as a control parameter. With Ch = 0.00127 the calculated melt equals the observed melt, which is 17.70 m w.e. over the 3 years. When averaged over the time when melting occurs (i.e. 35% of the time), the mean surface heat flux equals 191 W m−2. Net shortwave radiation contributes 177 W m−2, net longwave radiation −25 W m−2, the sensible-heat flux 31 W m−2 and the latent-heat flux 8 W m−2.

Buried layers of surface hoar are the failure plane for many slab avalanches, including fatal human-triggered avalanches in various mountain regions. These layers may persist as weak layers in the snow cover for weeks or months. It is therefore essential for operational avalanche forecasters to monitor the evolution of persistent weak layers, such as buried surface hoar. Traditional grain-shape observations of isolated grains with a magnifier and crystal screen do not show bonding that is decisive for strength. In this study we used in situ microphotography and observations of texture to complement strength measurements from shear frame tests. Buried layers of surface hoar consist of crystals most of which extend from the layer below to the layer above, and may exhibit a columnar or truss-like structure. Observations and measurements show that texture and crystal size change little over periods of up to several months during which the snowpack remains dry. Under these conditions, layer thickness decreases while density and strength increase. Based on field measurements, we argue that the increase in strength is primarily due to penetration of the surface-hoar crystals into the adjacent layers, especially at the bottom of the buried surface-hoar layer, where bonding is critical. The weak bonding at the bottom implies that shear failure occurs at the lower interface rather than within the weak layer. On slopes, we find that surface-hoar crystals that were initially surface-normal are tilted downslope faster than predicted by published shear strain rates for settled snow, indicating that shear strain is concentrated in these layers. The characteristic texture of buried surface hoar (columnar or truss-like) permits collapsing at the time of fracture. The gravitational energy released by the displacement of the slab may contribute to the extensive fracture propagation associated with buried surface-hoar layers.

A three-dimensional finite-element model is used to analyze field data collected as dirty basal ice flowed past an instrumented obstacle at the bed of Engabreen, a temperate glacier in northern Norway The ice is modeled as an incompressible power-law fluid, with viscosity , where ΠD is the second invariant of the stretching tensor, and B and n are two parameters. Using measurements obtained in 1996 and 1997, two values of B are obtained, one using the measured normal stress difference across the obstacle, and the other using the measured bed-parallel force over the instrument. These two values are not equal, probably owing to small frictional forces at the bed unaccounted for in the numerical model. Hence, B ranges between 1.9 × 107 and 3.2 × 107 Pa s1/3 in 1996, and between 2.2 × 107 and 4.1 × 107 Pa s1/3 in 1997. These values are smaller than measured elsewhere for clean glacier or laboratory ice. Field measurements of water content, fabric and texture of the basal ice suggest that unbound water between thin sediment layers and lamellae of clean ice may act as a lubricant and significantly weaken the ice. Near-isotropic fabrics indicate that preferred fabric orientation does not enhance the deformation.

We analyzed the possible controls on the distribution of surge-type glaciers in Svalbard using multivariate logit models including 504 glaciers and a large number of glacial and geological attributes. Specifically we examined the potential effect of geological boundaries, mass-balance conditions and thermal regime on surging. It was found that long glaciers with relatively steep slopes overlying young fine-grained sedimentary lithologies with orientations in a broad arc clockwise from northwest to southeast are most likely to be of surge type. No relation between lithological boundaries and surge potential could be established. Possible explanations for length being conducive to surging are transport-distance-related substrate properties, distance-related attenuation of longitudinal stresses and the possible relation between thermal regime and glacier size. Analysis of glaciers with recorded radioecho sounding reveals that a polythermal regime, accumulation-area ratios close to balance and a large elevation span increase the surge potential. The logit models also enabled us to detect 19 new surge-type glaciers, to reclassify six glaciers as normal and to identify unusual surge-type glaciers. Our model results suggest that a polythermal regime and fine-grained potentially deformable beds are conducive to the surge potential of Svalbard glaciers.